15q=92/5q

Solution for 15q=92/5q equation:

15q=92/5q

We move all terms to the left:

15q-(92/5q)=0


Domain of the equation: 5q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

15q-(+92/5q)=0

We get rid of parentheses

15q-92/5q=0

We multiply all the terms by the denominator


15q*5q-92=0

Wy multiply elements

75q^2-92=0

a = 75; b = 0; c = -92;
Δ = b2-4ac
Δ = 02-4·75·(-92)
Δ = 27600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{27600}=\sqrt{400*69}=\sqrt{400}*\sqrt{69}=20\sqrt{69}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{69}}{2*75}=\frac{0-20\sqrt{69}}{150}
=-\frac{20\sqrt{69}}{150}
=-\frac{2\sqrt{69}}{15}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{69}}{2*75}=\frac{0+20\sqrt{69}}{150}
=\frac{20\sqrt{69}}{150}
=\frac{2\sqrt{69}}{15}
$